Question: Complete the recursive formula of the geometric sequence $-1.5\,,\,6\,,-24\,,\,96,...$. $d(1)=$
Answer: The first term is $-1.5$ and the common ratio is $-4$. ${\times (-4)\,\curvearrowright}$ ${\times (-4)\,\curvearrowright}$ ${\times (-4)\,\curvearrowright}$ $-1.5,$ $6,$ $-24,$ $96,...$ This is the recursive formula of $-1.5\,,\,6\,,-24\,,\,96,...$. $\begin{cases} d(1)=-1.5 \\\\ d(n)=d(n-1)\cdot(-4) \end{cases}$